Answer to Q73
If a brick weighs 3kg plus half of a similar brick. How much does a brick and a half weigh?
If a brick weighs 3kg plus half of a similar brick, we can write this as an equation:
Let brick weight be x, so
x = 3kg + ½x
We can now find x
x = (6+x) ÷ 2
2x = 6+x
x = 6kg
So a brick weighs 6kg
How much does a brick and a half weigh?
Now since a brick weighs 6kg, half a brick will weigh 3kg
So, a brick and half will weigh 6 + 3 = 9
Answer: 9kg
If a brick weighs 3kg plus half of a similar brick. How much does a brick and a half weigh?
If a brick weighs 3kg plus half of a similar brick, we can write this as an equation:
Let brick weight be x, so
x = 3kg + ½x
We can now find x
x = (6+x) ÷ 2
2x = 6+x
x = 6kg
So a brick weighs 6kg
How much does a brick and a half weigh?
Now since a brick weighs 6kg, half a brick will weigh 3kg
So, a brick and half will weigh 6 + 3 = 9
Answer: 9kg
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Answer to Q74
My sister was half my age when I was 12, when I was 30 she got married and had her daughter a year later. I am now 70, how old is my niece?
My sister was half my age when I was 12:
That means my sister is 6 years younger than me.
when I was 30 she got married:
If she is 6 years younger than me, that means she got married at 24
and had her daughter a year later:
She had her daughter at 25
I am now 70, how old is my niece?
If I am 70 now, that means my sister is now 64. She gave birth at 25. Her daughter, my niece will now be 64 - 25 = 39
Answer: 39
My sister was half my age when I was 12, when I was 30 she got married and had her daughter a year later. I am now 70, how old is my niece?
My sister was half my age when I was 12:
That means my sister is 6 years younger than me.
when I was 30 she got married:
If she is 6 years younger than me, that means she got married at 24
and had her daughter a year later:
She had her daughter at 25
I am now 70, how old is my niece?
If I am 70 now, that means my sister is now 64. She gave birth at 25. Her daughter, my niece will now be 64 - 25 = 39
Answer: 39
Answer to Q75
[8, 2, 20], [10, 5, 52], [6, 3, 20], [4, 2, x]
[A, B, C]: C = (A x B) + (A ÷ B)
[8, 2, 20]: (8 x 2) + (8 ÷ 2) = 16 + 4 = 20
[10, 5, 52]: (10 x 5) + (10 ÷ 5) = 50 + 2 = 52
[6, 3, 20]: (6 x 3) + (6 ÷ 3) = 18 + 2 = 20
[4, 2, x]: x = (4 x 2) + (4 ÷ 2) = 8 + 2 = 10
Answer: 10
[8, 2, 20], [10, 5, 52], [6, 3, 20], [4, 2, x]
[A, B, C]: C = (A x B) + (A ÷ B)
[8, 2, 20]: (8 x 2) + (8 ÷ 2) = 16 + 4 = 20
[10, 5, 52]: (10 x 5) + (10 ÷ 5) = 50 + 2 = 52
[6, 3, 20]: (6 x 3) + (6 ÷ 3) = 18 + 2 = 20
[4, 2, x]: x = (4 x 2) + (4 ÷ 2) = 8 + 2 = 10
Answer: 10
Number of digit 3 bewteen 300 and 400.html
611 B
Answer to Q76:
If I wrote all the numbers from 300 to 400 on a piece of paper, how many times did I write the digit 3?
We all can write 300 to 400 and bring the numbers all together looks like this
300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400
We can now count the number of times 3 occurs. I don't have to manually do that so I wrote a little javascript code for that.
Answer: 120
If I wrote all the numbers from 300 to 400 on a piece of paper, how many times did I write the digit 3?
We all can write 300 to 400 and bring the numbers all together looks like this
300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400
We can now count the number of times 3 occurs. I don't have to manually do that so I wrote a little javascript code for that.
Answer: 120
Answer to Q77
In sharing a bottle of coke with my two sons, Tom and Harry. Tom brought a 3cm diameter, 6cm tall cup which I filled to the brim. Harry brought a 6cm diameter, 3cm tall cup which I also filled to the brim.
Who had the most coke?
Volume of Tom's cup:
Height of cup = 6cm
Diameter of cup = 3cm
Radius (r) = 1.5cm
Volume = πr²h
= π x 1.5² x 6
= 42.41cm³
Volume of Harry's cup:
Height of cup = 3cm
Diameter of cup = 6cm
Radius (r) = 3cm
Volume = πr²h
= π x 3² x 3
= 84.82cm³
Not only did Harry had more coke, he had exactly twice of Tom's coke.
Answer: Harry
Moral: This question is very similar to Q55, diameter matters alot.
In sharing a bottle of coke with my two sons, Tom and Harry. Tom brought a 3cm diameter, 6cm tall cup which I filled to the brim. Harry brought a 6cm diameter, 3cm tall cup which I also filled to the brim.
Who had the most coke?
Volume of Tom's cup:
Height of cup = 6cm
Diameter of cup = 3cm
Radius (r) = 1.5cm
Volume = πr²h
= π x 1.5² x 6
= 42.41cm³
Volume of Harry's cup:
Height of cup = 3cm
Diameter of cup = 6cm
Radius (r) = 3cm
Volume = πr²h
= π x 3² x 3
= 84.82cm³
Not only did Harry had more coke, he had exactly twice of Tom's coke.
Answer: Harry
Moral: This question is very similar to Q55, diameter matters alot.
Answer to Q78
12am is what?
AM is short for Ante Meridiem which means before noon, so 12am is the 12 before noon (i.e. 12 midnight)
Answer: 12 midnight
12am is what?
AM is short for Ante Meridiem which means before noon, so 12am is the 12 before noon (i.e. 12 midnight)
Answer: 12 midnight
Answer to Q79
[6, 7, 11, 20] [5, 3, 2] [x, 4] [10]. What is x?
Let's rewrite the series like this:
[A, B, C, D] [E, F, G] [H, I] [J]
Then:
E, A, B
F, B, C
G, C, D
H, E, F
I, F, G
J, H, I
all forms sub - series.
Let's test the theory,
5, 6, 7 that's a series with difference of 1
3, 7, 11 that's a series with difference of 4
2, 11, 20 that's a series with difference of 9
x, 5, 3 (5 and 3 has a difference of 2 so x should be 5 + 2 = 7)
4, 3, 2 that's a series with difference of -1
10, x, 4 (10 - 4 is 6 so the difference here can only be 6 ÷ 2 = 3) so series becomes 10, 7, 4. x was also 7 in our x, 5, 3 which means we are correct.
Answer: 7
[6, 7, 11, 20] [5, 3, 2] [x, 4] [10]. What is x?
Let's rewrite the series like this:
[A, B, C, D] [E, F, G] [H, I] [J]
Then:
E, A, B
F, B, C
G, C, D
H, E, F
I, F, G
J, H, I
all forms sub - series.
Let's test the theory,
5, 6, 7 that's a series with difference of 1
3, 7, 11 that's a series with difference of 4
2, 11, 20 that's a series with difference of 9
x, 5, 3 (5 and 3 has a difference of 2 so x should be 5 + 2 = 7)
4, 3, 2 that's a series with difference of -1
10, x, 4 (10 - 4 is 6 so the difference here can only be 6 ÷ 2 = 3) so series becomes 10, 7, 4. x was also 7 in our x, 5, 3 which means we are correct.
Answer: 7
Answer to Q80
[9, 25, 49, x] [7, 10, 15, 8, 7]. What is x?
Let's rewrite the series as [A, B, C, D] [E, F, G, H, I]
(F - E)² = A : (10 - 7)² = 9
(G - F)² = B : (15 - 10)² = 25
(H - G)² = C : (8 - 15)² = 49
(I - H)² = D : (7 - 8)² = 1
Answer: 1
[9, 25, 49, x] [7, 10, 15, 8, 7]. What is x?
Let's rewrite the series as [A, B, C, D] [E, F, G, H, I]
(F - E)² = A : (10 - 7)² = 9
(G - F)² = B : (15 - 10)² = 25
(H - G)² = C : (8 - 15)² = 49
(I - H)² = D : (7 - 8)² = 1
Answer: 1
Answer to Q81
A + B - C = 6; A - B + C = 8. What is A?
A + B - C = 6 (eqn i)
A - B + C = 8 (eqn ii)
Add eqn i to eqn ii, it becomes
2A = 14
A = 14 ÷ 2
A = 7
Answer: 7
A + B - C = 6; A - B + C = 8. What is A?
A + B - C = 6 (eqn i)
A - B + C = 8 (eqn ii)
Add eqn i to eqn ii, it becomes
2A = 14
A = 14 ÷ 2
A = 7
Answer: 7
Answer to Q82
A - 4B + 2C = 16, 2A + 7B - 5C = 83. What is A + B - C?
A - 4B + 2C = 16 (eqn i)
2A + 7B - 5C = 83 (eqn ii)
A + B - C (eqn iii)
Multiply (eqn i) by 2
2A - 8B + 4C = 32 (eqn iv)
Subtract (eqn ii) from (eqn iv)
-15B + 9C = -51
C = (-51 + 15B) ÷ 9 (eqn v)
Putting (eqn v) into (eqn i)
A - 4B - (102 ÷ 9) + (30B ÷ 9) = 16
A = 16 + 4B + (102 ÷ 9) - (30B ÷ 9) (eqn vi)
Putting (eqn vi) and (eqn v) into (eqn iii)
16 + 4B + (102 ÷ 9) - (30B ÷ 9) + B + (51÷ 9) - (15B ÷ 9)
Making 9 the common factor
(144 + 36B - 30B + 102 + 9B + 51 - 15B) ÷ 9
297 ÷ 9
= 33
Answer: 33
A - 4B + 2C = 16, 2A + 7B - 5C = 83. What is A + B - C?
A - 4B + 2C = 16 (eqn i)
2A + 7B - 5C = 83 (eqn ii)
A + B - C (eqn iii)
Multiply (eqn i) by 2
2A - 8B + 4C = 32 (eqn iv)
Subtract (eqn ii) from (eqn iv)
-15B + 9C = -51
C = (-51 + 15B) ÷ 9 (eqn v)
Putting (eqn v) into (eqn i)
A - 4B - (102 ÷ 9) + (30B ÷ 9) = 16
A = 16 + 4B + (102 ÷ 9) - (30B ÷ 9) (eqn vi)
Putting (eqn vi) and (eqn v) into (eqn iii)
16 + 4B + (102 ÷ 9) - (30B ÷ 9) + B + (51÷ 9) - (15B ÷ 9)
Making 9 the common factor
(144 + 36B - 30B + 102 + 9B + 51 - 15B) ÷ 9
297 ÷ 9
= 33
Answer: 33
Answer to Q83
1, 3, 8, 19, x. What is x?
Finding the difference between this series:
3 - 1 = 2
8 - 3 = 5
19 - 8 = 11
x - 19 = y (eqn i)
We have a new series here:
2, 5, 11, y and there still didn't seem to be a clear relationship between them, so we find their difference again.
5 - 2 = 3
11 - 5 = 6
y - 11 = z (eqn ii)
New series 3, 6, z so here we have our relationship. First element is 3, second element is twice of first element (2x3 = 6), so
z = 6 x 2 = 12
Putting z into eqn ii
y - 11 = 12
y = 12 + 11 = 23
Putting y into eqn i
x - 19 = 23
x = 23 + 19 = 42
Answer: 42
1, 3, 8, 19, x. What is x?
Finding the difference between this series:
3 - 1 = 2
8 - 3 = 5
19 - 8 = 11
x - 19 = y (eqn i)
We have a new series here:
2, 5, 11, y and there still didn't seem to be a clear relationship between them, so we find their difference again.
5 - 2 = 3
11 - 5 = 6
y - 11 = z (eqn ii)
New series 3, 6, z so here we have our relationship. First element is 3, second element is twice of first element (2x3 = 6), so
z = 6 x 2 = 12
Putting z into eqn ii
y - 11 = 12
y = 12 + 11 = 23
Putting y into eqn i
x - 19 = 23
x = 23 + 19 = 42
Answer: 42
Answer to Q84
528 = 15, 703 = 10, 397 = 19, 601 = x. What is x?
ABC = A+B+C
528 = 5 + 2 + 8 = 15
703 = 7 + 0 + 3 = 10
397 = 3 + 9 + 7 = 19
601 = 6 + 0 + 1 = 7
Answer: 7
528 = 15, 703 = 10, 397 = 19, 601 = x. What is x?
ABC = A+B+C
528 = 5 + 2 + 8 = 15
703 = 7 + 0 + 3 = 10
397 = 3 + 9 + 7 = 19
601 = 6 + 0 + 1 = 7
Answer: 7
Answer to Q85
Is a - b - c = a - (b - c)?
This question generates from a mistake I made while in a rush to do the calculation 18 - 3 - 2. Immediately I saw the question, I (been in a hurray and not thinking clearly) did a stupid 3 - 2 = 1; 18 - 1 = 17
Immediately I saw my answer, my instinct told me something is wrong with it. then I saw my mistake!
What I should have done was -3-2 = -5; 18 - 5 = 13!
a - b - c can not be equals to a - (b - c)
Expanding a - (b - c) will give you a -b -(-c) = a - b + c
That was why I got 17 earlier (18 - 3 + 2)
Answer: False
Is a - b - c = a - (b - c)?
This question generates from a mistake I made while in a rush to do the calculation 18 - 3 - 2. Immediately I saw the question, I (been in a hurray and not thinking clearly) did a stupid 3 - 2 = 1; 18 - 1 = 17
Immediately I saw my answer, my instinct told me something is wrong with it. then I saw my mistake!
What I should have done was -3-2 = -5; 18 - 5 = 13!
a - b - c can not be equals to a - (b - c)
Expanding a - (b - c) will give you a -b -(-c) = a - b + c
That was why I got 17 earlier (18 - 3 + 2)
Answer: False
Answer to Q86
What are the three consecutive integers whose sum are equal to 93?
Let the first integer be x. The consecutive integers will then be x+1 and x+2.
So, x + (x+1) + (x+2) = 93
x + x+1 + x+2 = 93
3x + 3 = 93
3x = 93 - 3
3x = 90
x = 90 ÷ 3
x = 30
So, first integer is 30.
Answer: 30, 31, 32
What are the three consecutive integers whose sum are equal to 93?
Let the first integer be x. The consecutive integers will then be x+1 and x+2.
So, x + (x+1) + (x+2) = 93
x + x+1 + x+2 = 93
3x + 3 = 93
3x = 93 - 3
3x = 90
x = 90 ÷ 3
x = 30
So, first integer is 30.
Answer: 30, 31, 32
Answer to Q87
A+B=36; A-B=24; A÷B=?
A + B = 36 - - (i)
A - B = 24 - - (ii)
A ÷ B = ?
From (i)
B = 36 - A - - (iii)
Putting (iii) into (ii)
A - (36 - A) = 24
A - 36 + A = 24
2A = 24 + 36
2A = 60
A = 30
Putting A into (iii)
B = 36 - 30
B = 6
So, A ÷ B = 30 ÷ 6 = 5
Answer: 5
A+B=36; A-B=24; A÷B=?
A + B = 36 - - (i)
A - B = 24 - - (ii)
A ÷ B = ?
From (i)
B = 36 - A - - (iii)
Putting (iii) into (ii)
A - (36 - A) = 24
A - 36 + A = 24
2A = 24 + 36
2A = 60
A = 30
Putting A into (iii)
B = 36 - 30
B = 6
So, A ÷ B = 30 ÷ 6 = 5
Answer: 5
Answer to Q88
A flock of birds flying met a single bird.
The single bird greeted the flock "hello hundred" but the flock replied "we are not hundred, half of us plus you will make us hundred". How many birds were flying?
Let the number of birds in the flock be x
But half of x plus 1 will make a hundred
so,
(x ÷ 2) + 1 = 100
x ÷ 2 = 99
x = 99 * 2
x = 198
So, number of birds in the flock is 198.
But here is the tricky part, the question asked "How many birds were flying?" NOT "What is the number of birds in the flock?". The single bird that greeted the flock was also flying (if he wasn't flying how would he have met the flying flock?).
So, number of birds flying = number of flock + single bird
= 198 + 1
= 199
Answer: 199
A flock of birds flying met a single bird.
The single bird greeted the flock "hello hundred" but the flock replied "we are not hundred, half of us plus you will make us hundred". How many birds were flying?
Let the number of birds in the flock be x
But half of x plus 1 will make a hundred
so,
(x ÷ 2) + 1 = 100
x ÷ 2 = 99
x = 99 * 2
x = 198
So, number of birds in the flock is 198.
But here is the tricky part, the question asked "How many birds were flying?" NOT "What is the number of birds in the flock?". The single bird that greeted the flock was also flying (if he wasn't flying how would he have met the flying flock?).
So, number of birds flying = number of flock + single bird
= 198 + 1
= 199
Answer: 199
Answer to Q89
Add me to myself and multiply by 4. Divide me by 8 and you will have me once more. What number am I?
Let myself be x
Add me to myself: x + x = 2x
And multiply by 4: 4(2x) = 8x
Then divide by 8: 8x ÷ 8 = x
Answer: Any number in the world!
Add me to myself and multiply by 4. Divide me by 8 and you will have me once more. What number am I?
Let myself be x
Add me to myself: x + x = 2x
And multiply by 4: 4(2x) = 8x
Then divide by 8: 8x ÷ 8 = x
Answer: Any number in the world!
Answer to Q90
Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?
Let Sally's age be x
Let her mother's age be y
Now, x = 54 and y = 80
So, y - x = 26 (the mother will always be 26 years older than Sally at all time)
But there was a time when the mother's age was three times Sally's age.
So at that time: y = 3x - - eq i
But remember: y - x = 26 - - eq ii
From eq ii
y = 26 + x - - eq iii
Putting eq iii into eq i
26 + x = 3x
26 = 3x - x
26 = 2x
x = 26 ÷ 2
x = 13
So, when Sally was 13 her mother was 3 x 13 = 39. And to check, is 39 - 13, 26? Yes, so we are good.
But here is the tricky part, the question asked for how many years ago that scenario was not Sally's age at that time.
Sally is now 54 and the scenario was when she was 13, so that was 54 - 13 years ago
Answer: 41
Sally is 54 years old and her mother is 80, how many years ago was Sally's mother three times her age?
Let Sally's age be x
Let her mother's age be y
Now, x = 54 and y = 80
So, y - x = 26 (the mother will always be 26 years older than Sally at all time)
But there was a time when the mother's age was three times Sally's age.
So at that time: y = 3x - - eq i
But remember: y - x = 26 - - eq ii
From eq ii
y = 26 + x - - eq iii
Putting eq iii into eq i
26 + x = 3x
26 = 3x - x
26 = 2x
x = 26 ÷ 2
x = 13
So, when Sally was 13 her mother was 3 x 13 = 39. And to check, is 39 - 13, 26? Yes, so we are good.
But here is the tricky part, the question asked for how many years ago that scenario was not Sally's age at that time.
Sally is now 54 and the scenario was when she was 13, so that was 54 - 13 years ago
Answer: 41
Answer to Q91
What is half of two plus two?
This question is more of a logical question, the answer depends on how you interpret the question. So, logically speaking, what's the difference between:
A: What is half of two plus two?
B: What is the half of the summation of two and two?
Logically, A is telling you to half two and add it to two ((2÷2) + 2 = 3) while B is telling you to half the summation of two and two ( (2 + 2) ÷ 2 = 2)
Answer: 3 (but again, it all depends on your logic)
What is half of two plus two?
This question is more of a logical question, the answer depends on how you interpret the question. So, logically speaking, what's the difference between:
A: What is half of two plus two?
B: What is the half of the summation of two and two?
Logically, A is telling you to half two and add it to two ((2÷2) + 2 = 3) while B is telling you to half the summation of two and two ( (2 + 2) ÷ 2 = 2)
Answer: 3 (but again, it all depends on your logic)
Answer to Q92
In two years I know, I'll be twice as old as five years ago, said Tom. How old is Tom?
Let Tom's current age be y
But in 2 years time (y + 2), Tom will be twice is age five years ago (y - 5)
(y + 2) = 2 x (y - 5)
y + 2 = 2y - 10
2 + 10 = 2y - y
12 = y
So, Tom is currently 12
Answer: 12
In two years I know, I'll be twice as old as five years ago, said Tom. How old is Tom?
Let Tom's current age be y
But in 2 years time (y + 2), Tom will be twice is age five years ago (y - 5)
(y + 2) = 2 x (y - 5)
y + 2 = 2y - 10
2 + 10 = 2y - y
12 = y
So, Tom is currently 12
Answer: 12
Answer to Q92
Mom and dad have four daughters, and each daughter has one brother. How many people are in the family?
Mom and dad have four daughters, so number of daughters = 4
Each daughters has one brother, this is the tricky part. If each daughters has one brother, this means there is just one brother in the family.
Say there is a Brother Z and Sisters A, B, C and D. Z is a brother to all A, B, C and D not just A or B.
So, number of sons = 1
How many people are in the family = daughters + son + dad + mom = 4 + 1 + 1 + 1 = 7
Answer: 7
Mom and dad have four daughters, and each daughter has one brother. How many people are in the family?
Mom and dad have four daughters, so number of daughters = 4
Each daughters has one brother, this is the tricky part. If each daughters has one brother, this means there is just one brother in the family.
Say there is a Brother Z and Sisters A, B, C and D. Z is a brother to all A, B, C and D not just A or B.
So, number of sons = 1
How many people are in the family = daughters + son + dad + mom = 4 + 1 + 1 + 1 = 7
Answer: 7